
The distance-based spatial encoding is the most critical term in node encoding. Without this term, the AUC decreases sharply to about \(50\%\) , which indicates that the anomalies become indistinguishable. Such a phenomenon proves that the local structural information is significant in detecting anomalies, which is also pointed out in previous works [1]}, [2]}.

The diffusion-based spatial encoding and relative temporal encoding both have a minor contribution in detecting anomalies. In the vast majority of cases, removing one of them would lead to a slight performance drop. We infer from the results that the diffusion-based spatial encoding provides a global view for graph structure which has a minor relation to anomaly detection. Moreover, the temporal encoding points out the occurrence time of neighborhoods which is relatively unimportant since the nodes have been selected to the substructure set.

In most of the cases, combining all of the three types of encoding has the highest AUC, excepted on UCI Messages dataset. This shows that using a comprehensive spatial-temporal encoding is meaningful to anomaly detection. As for the exception, we guess that emphasizing the relative time distance may lead to an over-fitting on such property in some cases, which further results in a slight side effect on performance.

